1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 153,678 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 153,668 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      7
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      3
## 111  2020-06-19          East of England      5
## 112  2020-06-20          East of England      0
## 113  2020-03-01                   London      0
## 114  2020-03-02                   London      0
## 115  2020-03-03                   London      0
## 116  2020-03-04                   London      0
## 117  2020-03-05                   London      0
## 118  2020-03-06                   London      1
## 119  2020-03-07                   London      0
## 120  2020-03-08                   London      0
## 121  2020-03-09                   London      1
## 122  2020-03-10                   London      0
## 123  2020-03-11                   London      6
## 124  2020-03-12                   London      6
## 125  2020-03-13                   London     10
## 126  2020-03-14                   London     14
## 127  2020-03-15                   London     10
## 128  2020-03-16                   London     15
## 129  2020-03-17                   London     23
## 130  2020-03-18                   London     27
## 131  2020-03-19                   London     25
## 132  2020-03-20                   London     44
## 133  2020-03-21                   London     49
## 134  2020-03-22                   London     54
## 135  2020-03-23                   London     63
## 136  2020-03-24                   London     87
## 137  2020-03-25                   London    113
## 138  2020-03-26                   London    129
## 139  2020-03-27                   London    130
## 140  2020-03-28                   London    122
## 141  2020-03-29                   London    146
## 142  2020-03-30                   London    149
## 143  2020-03-31                   London    181
## 144  2020-04-01                   London    202
## 145  2020-04-02                   London    190
## 146  2020-04-03                   London    196
## 147  2020-04-04                   London    230
## 148  2020-04-05                   London    195
## 149  2020-04-06                   London    197
## 150  2020-04-07                   London    220
## 151  2020-04-08                   London    238
## 152  2020-04-09                   London    206
## 153  2020-04-10                   London    170
## 154  2020-04-11                   London    178
## 155  2020-04-12                   London    158
## 156  2020-04-13                   London    166
## 157  2020-04-14                   London    144
## 158  2020-04-15                   London    142
## 159  2020-04-16                   London    139
## 160  2020-04-17                   London    100
## 161  2020-04-18                   London    101
## 162  2020-04-19                   London    103
## 163  2020-04-20                   London     95
## 164  2020-04-21                   London     94
## 165  2020-04-22                   London    109
## 166  2020-04-23                   London     77
## 167  2020-04-24                   London     71
## 168  2020-04-25                   London     58
## 169  2020-04-26                   London     53
## 170  2020-04-27                   London     51
## 171  2020-04-28                   London     43
## 172  2020-04-29                   London     44
## 173  2020-04-30                   London     40
## 174  2020-05-01                   London     41
## 175  2020-05-02                   London     41
## 176  2020-05-03                   London     36
## 177  2020-05-04                   London     30
## 178  2020-05-05                   London     25
## 179  2020-05-06                   London     37
## 180  2020-05-07                   London     37
## 181  2020-05-08                   London     30
## 182  2020-05-09                   London     23
## 183  2020-05-10                   London     26
## 184  2020-05-11                   London     18
## 185  2020-05-12                   London     18
## 186  2020-05-13                   London     16
## 187  2020-05-14                   London     20
## 188  2020-05-15                   London     18
## 189  2020-05-16                   London     14
## 190  2020-05-17                   London     15
## 191  2020-05-18                   London      9
## 192  2020-05-19                   London     14
## 193  2020-05-20                   London     19
## 194  2020-05-21                   London     12
## 195  2020-05-22                   London     10
## 196  2020-05-23                   London      6
## 197  2020-05-24                   London      7
## 198  2020-05-25                   London      9
## 199  2020-05-26                   London     12
## 200  2020-05-27                   London      7
## 201  2020-05-28                   London      8
## 202  2020-05-29                   London      7
## 203  2020-05-30                   London     12
## 204  2020-05-31                   London      6
## 205  2020-06-01                   London     10
## 206  2020-06-02                   London      7
## 207  2020-06-03                   London      6
## 208  2020-06-04                   London      8
## 209  2020-06-05                   London      4
## 210  2020-06-06                   London      0
## 211  2020-06-07                   London      4
## 212  2020-06-08                   London      5
## 213  2020-06-09                   London      4
## 214  2020-06-10                   London      7
## 215  2020-06-11                   London      5
## 216  2020-06-12                   London      3
## 217  2020-06-13                   London      3
## 218  2020-06-14                   London      2
## 219  2020-06-15                   London      1
## 220  2020-06-16                   London      2
## 221  2020-06-17                   London      1
## 222  2020-06-18                   London      2
## 223  2020-06-19                   London      0
## 224  2020-06-20                   London      0
## 225  2020-03-01                 Midlands      0
## 226  2020-03-02                 Midlands      0
## 227  2020-03-03                 Midlands      1
## 228  2020-03-04                 Midlands      0
## 229  2020-03-05                 Midlands      0
## 230  2020-03-06                 Midlands      0
## 231  2020-03-07                 Midlands      0
## 232  2020-03-08                 Midlands      3
## 233  2020-03-09                 Midlands      1
## 234  2020-03-10                 Midlands      0
## 235  2020-03-11                 Midlands      2
## 236  2020-03-12                 Midlands      6
## 237  2020-03-13                 Midlands      5
## 238  2020-03-14                 Midlands      4
## 239  2020-03-15                 Midlands      5
## 240  2020-03-16                 Midlands     11
## 241  2020-03-17                 Midlands      8
## 242  2020-03-18                 Midlands     13
## 243  2020-03-19                 Midlands      8
## 244  2020-03-20                 Midlands     28
## 245  2020-03-21                 Midlands     13
## 246  2020-03-22                 Midlands     31
## 247  2020-03-23                 Midlands     33
## 248  2020-03-24                 Midlands     41
## 249  2020-03-25                 Midlands     48
## 250  2020-03-26                 Midlands     64
## 251  2020-03-27                 Midlands     72
## 252  2020-03-28                 Midlands     89
## 253  2020-03-29                 Midlands     92
## 254  2020-03-30                 Midlands     90
## 255  2020-03-31                 Midlands    123
## 256  2020-04-01                 Midlands    140
## 257  2020-04-02                 Midlands    142
## 258  2020-04-03                 Midlands    124
## 259  2020-04-04                 Midlands    151
## 260  2020-04-05                 Midlands    164
## 261  2020-04-06                 Midlands    140
## 262  2020-04-07                 Midlands    123
## 263  2020-04-08                 Midlands    186
## 264  2020-04-09                 Midlands    139
## 265  2020-04-10                 Midlands    127
## 266  2020-04-11                 Midlands    142
## 267  2020-04-12                 Midlands    139
## 268  2020-04-13                 Midlands    120
## 269  2020-04-14                 Midlands    116
## 270  2020-04-15                 Midlands    147
## 271  2020-04-16                 Midlands    102
## 272  2020-04-17                 Midlands    118
## 273  2020-04-18                 Midlands    115
## 274  2020-04-19                 Midlands     92
## 275  2020-04-20                 Midlands    107
## 276  2020-04-21                 Midlands     86
## 277  2020-04-22                 Midlands     78
## 278  2020-04-23                 Midlands    103
## 279  2020-04-24                 Midlands     79
## 280  2020-04-25                 Midlands     72
## 281  2020-04-26                 Midlands     81
## 282  2020-04-27                 Midlands     74
## 283  2020-04-28                 Midlands     68
## 284  2020-04-29                 Midlands     53
## 285  2020-04-30                 Midlands     56
## 286  2020-05-01                 Midlands     64
## 287  2020-05-02                 Midlands     51
## 288  2020-05-03                 Midlands     52
## 289  2020-05-04                 Midlands     61
## 290  2020-05-05                 Midlands     58
## 291  2020-05-06                 Midlands     59
## 292  2020-05-07                 Midlands     48
## 293  2020-05-08                 Midlands     34
## 294  2020-05-09                 Midlands     37
## 295  2020-05-10                 Midlands     42
## 296  2020-05-11                 Midlands     33
## 297  2020-05-12                 Midlands     45
## 298  2020-05-13                 Midlands     40
## 299  2020-05-14                 Midlands     37
## 300  2020-05-15                 Midlands     40
## 301  2020-05-16                 Midlands     34
## 302  2020-05-17                 Midlands     31
## 303  2020-05-18                 Midlands     34
## 304  2020-05-19                 Midlands     34
## 305  2020-05-20                 Midlands     36
## 306  2020-05-21                 Midlands     32
## 307  2020-05-22                 Midlands     27
## 308  2020-05-23                 Midlands     34
## 309  2020-05-24                 Midlands     19
## 310  2020-05-25                 Midlands     26
## 311  2020-05-26                 Midlands     33
## 312  2020-05-27                 Midlands     29
## 313  2020-05-28                 Midlands     27
## 314  2020-05-29                 Midlands     20
## 315  2020-05-30                 Midlands     20
## 316  2020-05-31                 Midlands     22
## 317  2020-06-01                 Midlands     20
## 318  2020-06-02                 Midlands     22
## 319  2020-06-03                 Midlands     24
## 320  2020-06-04                 Midlands     15
## 321  2020-06-05                 Midlands     21
## 322  2020-06-06                 Midlands     20
## 323  2020-06-07                 Midlands     16
## 324  2020-06-08                 Midlands     15
## 325  2020-06-09                 Midlands     17
## 326  2020-06-10                 Midlands     15
## 327  2020-06-11                 Midlands     13
## 328  2020-06-12                 Midlands     12
## 329  2020-06-13                 Midlands      6
## 330  2020-06-14                 Midlands     17
## 331  2020-06-15                 Midlands     12
## 332  2020-06-16                 Midlands     13
## 333  2020-06-17                 Midlands     10
## 334  2020-06-18                 Midlands     14
## 335  2020-06-19                 Midlands      6
## 336  2020-06-20                 Midlands      2
## 337  2020-03-01 North East and Yorkshire      0
## 338  2020-03-02 North East and Yorkshire      0
## 339  2020-03-03 North East and Yorkshire      0
## 340  2020-03-04 North East and Yorkshire      0
## 341  2020-03-05 North East and Yorkshire      0
## 342  2020-03-06 North East and Yorkshire      0
## 343  2020-03-07 North East and Yorkshire      0
## 344  2020-03-08 North East and Yorkshire      0
## 345  2020-03-09 North East and Yorkshire      0
## 346  2020-03-10 North East and Yorkshire      0
## 347  2020-03-11 North East and Yorkshire      0
## 348  2020-03-12 North East and Yorkshire      0
## 349  2020-03-13 North East and Yorkshire      0
## 350  2020-03-14 North East and Yorkshire      0
## 351  2020-03-15 North East and Yorkshire      2
## 352  2020-03-16 North East and Yorkshire      3
## 353  2020-03-17 North East and Yorkshire      1
## 354  2020-03-18 North East and Yorkshire      2
## 355  2020-03-19 North East and Yorkshire      6
## 356  2020-03-20 North East and Yorkshire      5
## 357  2020-03-21 North East and Yorkshire      6
## 358  2020-03-22 North East and Yorkshire      7
## 359  2020-03-23 North East and Yorkshire      9
## 360  2020-03-24 North East and Yorkshire      8
## 361  2020-03-25 North East and Yorkshire     18
## 362  2020-03-26 North East and Yorkshire     21
## 363  2020-03-27 North East and Yorkshire     28
## 364  2020-03-28 North East and Yorkshire     35
## 365  2020-03-29 North East and Yorkshire     38
## 366  2020-03-30 North East and Yorkshire     64
## 367  2020-03-31 North East and Yorkshire     60
## 368  2020-04-01 North East and Yorkshire     67
## 369  2020-04-02 North East and Yorkshire     74
## 370  2020-04-03 North East and Yorkshire    100
## 371  2020-04-04 North East and Yorkshire    105
## 372  2020-04-05 North East and Yorkshire     92
## 373  2020-04-06 North East and Yorkshire     96
## 374  2020-04-07 North East and Yorkshire    102
## 375  2020-04-08 North East and Yorkshire    107
## 376  2020-04-09 North East and Yorkshire    111
## 377  2020-04-10 North East and Yorkshire    117
## 378  2020-04-11 North East and Yorkshire     98
## 379  2020-04-12 North East and Yorkshire     84
## 380  2020-04-13 North East and Yorkshire     94
## 381  2020-04-14 North East and Yorkshire    107
## 382  2020-04-15 North East and Yorkshire     96
## 383  2020-04-16 North East and Yorkshire    103
## 384  2020-04-17 North East and Yorkshire     88
## 385  2020-04-18 North East and Yorkshire     95
## 386  2020-04-19 North East and Yorkshire     88
## 387  2020-04-20 North East and Yorkshire    100
## 388  2020-04-21 North East and Yorkshire     76
## 389  2020-04-22 North East and Yorkshire     84
## 390  2020-04-23 North East and Yorkshire     63
## 391  2020-04-24 North East and Yorkshire     72
## 392  2020-04-25 North East and Yorkshire     69
## 393  2020-04-26 North East and Yorkshire     65
## 394  2020-04-27 North East and Yorkshire     65
## 395  2020-04-28 North East and Yorkshire     57
## 396  2020-04-29 North East and Yorkshire     69
## 397  2020-04-30 North East and Yorkshire     57
## 398  2020-05-01 North East and Yorkshire     64
## 399  2020-05-02 North East and Yorkshire     48
## 400  2020-05-03 North East and Yorkshire     40
## 401  2020-05-04 North East and Yorkshire     49
## 402  2020-05-05 North East and Yorkshire     40
## 403  2020-05-06 North East and Yorkshire     51
## 404  2020-05-07 North East and Yorkshire     45
## 405  2020-05-08 North East and Yorkshire     42
## 406  2020-05-09 North East and Yorkshire     44
## 407  2020-05-10 North East and Yorkshire     40
## 408  2020-05-11 North East and Yorkshire     29
## 409  2020-05-12 North East and Yorkshire     27
## 410  2020-05-13 North East and Yorkshire     28
## 411  2020-05-14 North East and Yorkshire     30
## 412  2020-05-15 North East and Yorkshire     32
## 413  2020-05-16 North East and Yorkshire     35
## 414  2020-05-17 North East and Yorkshire     26
## 415  2020-05-18 North East and Yorkshire     29
## 416  2020-05-19 North East and Yorkshire     27
## 417  2020-05-20 North East and Yorkshire     21
## 418  2020-05-21 North East and Yorkshire     33
## 419  2020-05-22 North East and Yorkshire     22
## 420  2020-05-23 North East and Yorkshire     18
## 421  2020-05-24 North East and Yorkshire     25
## 422  2020-05-25 North East and Yorkshire     21
## 423  2020-05-26 North East and Yorkshire     21
## 424  2020-05-27 North East and Yorkshire     22
## 425  2020-05-28 North East and Yorkshire     20
## 426  2020-05-29 North East and Yorkshire     25
## 427  2020-05-30 North East and Yorkshire     20
## 428  2020-05-31 North East and Yorkshire     20
## 429  2020-06-01 North East and Yorkshire     16
## 430  2020-06-02 North East and Yorkshire     22
## 431  2020-06-03 North East and Yorkshire     22
## 432  2020-06-04 North East and Yorkshire     17
## 433  2020-06-05 North East and Yorkshire     17
## 434  2020-06-06 North East and Yorkshire     21
## 435  2020-06-07 North East and Yorkshire     13
## 436  2020-06-08 North East and Yorkshire     11
## 437  2020-06-09 North East and Yorkshire     11
## 438  2020-06-10 North East and Yorkshire     18
## 439  2020-06-11 North East and Yorkshire      7
## 440  2020-06-12 North East and Yorkshire      9
## 441  2020-06-13 North East and Yorkshire     10
## 442  2020-06-14 North East and Yorkshire     11
## 443  2020-06-15 North East and Yorkshire      8
## 444  2020-06-16 North East and Yorkshire     10
## 445  2020-06-17 North East and Yorkshire      6
## 446  2020-06-18 North East and Yorkshire      7
## 447  2020-06-19 North East and Yorkshire      2
## 448  2020-06-20 North East and Yorkshire      3
## 449  2020-03-01               North West      0
## 450  2020-03-02               North West      0
## 451  2020-03-03               North West      0
## 452  2020-03-04               North West      0
## 453  2020-03-05               North West      1
## 454  2020-03-06               North West      0
## 455  2020-03-07               North West      0
## 456  2020-03-08               North West      1
## 457  2020-03-09               North West      0
## 458  2020-03-10               North West      0
## 459  2020-03-11               North West      0
## 460  2020-03-12               North West      2
## 461  2020-03-13               North West      3
## 462  2020-03-14               North West      1
## 463  2020-03-15               North West      4
## 464  2020-03-16               North West      2
## 465  2020-03-17               North West      4
## 466  2020-03-18               North West      6
## 467  2020-03-19               North West      7
## 468  2020-03-20               North West     10
## 469  2020-03-21               North West     11
## 470  2020-03-22               North West     13
## 471  2020-03-23               North West     15
## 472  2020-03-24               North West     21
## 473  2020-03-25               North West     21
## 474  2020-03-26               North West     29
## 475  2020-03-27               North West     35
## 476  2020-03-28               North West     28
## 477  2020-03-29               North West     46
## 478  2020-03-30               North West     67
## 479  2020-03-31               North West     52
## 480  2020-04-01               North West     86
## 481  2020-04-02               North West     96
## 482  2020-04-03               North West     95
## 483  2020-04-04               North West     98
## 484  2020-04-05               North West    102
## 485  2020-04-06               North West    100
## 486  2020-04-07               North West    135
## 487  2020-04-08               North West    127
## 488  2020-04-09               North West    119
## 489  2020-04-10               North West    117
## 490  2020-04-11               North West    138
## 491  2020-04-12               North West    125
## 492  2020-04-13               North West    129
## 493  2020-04-14               North West    131
## 494  2020-04-15               North West    114
## 495  2020-04-16               North West    135
## 496  2020-04-17               North West     98
## 497  2020-04-18               North West    113
## 498  2020-04-19               North West     71
## 499  2020-04-20               North West     83
## 500  2020-04-21               North West     76
## 501  2020-04-22               North West     86
## 502  2020-04-23               North West     85
## 503  2020-04-24               North West     66
## 504  2020-04-25               North West     65
## 505  2020-04-26               North West     55
## 506  2020-04-27               North West     54
## 507  2020-04-28               North West     57
## 508  2020-04-29               North West     62
## 509  2020-04-30               North West     59
## 510  2020-05-01               North West     45
## 511  2020-05-02               North West     56
## 512  2020-05-03               North West     55
## 513  2020-05-04               North West     48
## 514  2020-05-05               North West     48
## 515  2020-05-06               North West     44
## 516  2020-05-07               North West     49
## 517  2020-05-08               North West     42
## 518  2020-05-09               North West     30
## 519  2020-05-10               North West     41
## 520  2020-05-11               North West     35
## 521  2020-05-12               North West     38
## 522  2020-05-13               North West     25
## 523  2020-05-14               North West     26
## 524  2020-05-15               North West     33
## 525  2020-05-16               North West     32
## 526  2020-05-17               North West     24
## 527  2020-05-18               North West     31
## 528  2020-05-19               North West     35
## 529  2020-05-20               North West     27
## 530  2020-05-21               North West     26
## 531  2020-05-22               North West     26
## 532  2020-05-23               North West     31
## 533  2020-05-24               North West     26
## 534  2020-05-25               North West     31
## 535  2020-05-26               North West     27
## 536  2020-05-27               North West     27
## 537  2020-05-28               North West     28
## 538  2020-05-29               North West     20
## 539  2020-05-30               North West     19
## 540  2020-05-31               North West     13
## 541  2020-06-01               North West     12
## 542  2020-06-02               North West     27
## 543  2020-06-03               North West     22
## 544  2020-06-04               North West     22
## 545  2020-06-05               North West     15
## 546  2020-06-06               North West     23
## 547  2020-06-07               North West     19
## 548  2020-06-08               North West     20
## 549  2020-06-09               North West     15
## 550  2020-06-10               North West     14
## 551  2020-06-11               North West     16
## 552  2020-06-12               North West      7
## 553  2020-06-13               North West      8
## 554  2020-06-14               North West     15
## 555  2020-06-15               North West     14
## 556  2020-06-16               North West     11
## 557  2020-06-17               North West     10
## 558  2020-06-18               North West      6
## 559  2020-06-19               North West      5
## 560  2020-06-20               North West      1
## 561  2020-03-01               South East      0
## 562  2020-03-02               South East      0
## 563  2020-03-03               South East      1
## 564  2020-03-04               South East      0
## 565  2020-03-05               South East      1
## 566  2020-03-06               South East      0
## 567  2020-03-07               South East      0
## 568  2020-03-08               South East      1
## 569  2020-03-09               South East      1
## 570  2020-03-10               South East      1
## 571  2020-03-11               South East      1
## 572  2020-03-12               South East      0
## 573  2020-03-13               South East      1
## 574  2020-03-14               South East      1
## 575  2020-03-15               South East      5
## 576  2020-03-16               South East      8
## 577  2020-03-17               South East      7
## 578  2020-03-18               South East     10
## 579  2020-03-19               South East      9
## 580  2020-03-20               South East     13
## 581  2020-03-21               South East      7
## 582  2020-03-22               South East     25
## 583  2020-03-23               South East     20
## 584  2020-03-24               South East     22
## 585  2020-03-25               South East     29
## 586  2020-03-26               South East     35
## 587  2020-03-27               South East     34
## 588  2020-03-28               South East     36
## 589  2020-03-29               South East     55
## 590  2020-03-30               South East     58
## 591  2020-03-31               South East     65
## 592  2020-04-01               South East     66
## 593  2020-04-02               South East     55
## 594  2020-04-03               South East     72
## 595  2020-04-04               South East     80
## 596  2020-04-05               South East     82
## 597  2020-04-06               South East     88
## 598  2020-04-07               South East    100
## 599  2020-04-08               South East     83
## 600  2020-04-09               South East    104
## 601  2020-04-10               South East     88
## 602  2020-04-11               South East     88
## 603  2020-04-12               South East     88
## 604  2020-04-13               South East     84
## 605  2020-04-14               South East     65
## 606  2020-04-15               South East     72
## 607  2020-04-16               South East     56
## 608  2020-04-17               South East     86
## 609  2020-04-18               South East     57
## 610  2020-04-19               South East     70
## 611  2020-04-20               South East     87
## 612  2020-04-21               South East     50
## 613  2020-04-22               South East     54
## 614  2020-04-23               South East     57
## 615  2020-04-24               South East     64
## 616  2020-04-25               South East     51
## 617  2020-04-26               South East     51
## 618  2020-04-27               South East     40
## 619  2020-04-28               South East     40
## 620  2020-04-29               South East     47
## 621  2020-04-30               South East     29
## 622  2020-05-01               South East     37
## 623  2020-05-02               South East     36
## 624  2020-05-03               South East     17
## 625  2020-05-04               South East     35
## 626  2020-05-05               South East     29
## 627  2020-05-06               South East     25
## 628  2020-05-07               South East     27
## 629  2020-05-08               South East     26
## 630  2020-05-09               South East     28
## 631  2020-05-10               South East     19
## 632  2020-05-11               South East     25
## 633  2020-05-12               South East     27
## 634  2020-05-13               South East     18
## 635  2020-05-14               South East     32
## 636  2020-05-15               South East     24
## 637  2020-05-16               South East     22
## 638  2020-05-17               South East     18
## 639  2020-05-18               South East     22
## 640  2020-05-19               South East     12
## 641  2020-05-20               South East     22
## 642  2020-05-21               South East     15
## 643  2020-05-22               South East     17
## 644  2020-05-23               South East     21
## 645  2020-05-24               South East     17
## 646  2020-05-25               South East     13
## 647  2020-05-26               South East     19
## 648  2020-05-27               South East     18
## 649  2020-05-28               South East     12
## 650  2020-05-29               South East     21
## 651  2020-05-30               South East      8
## 652  2020-05-31               South East     10
## 653  2020-06-01               South East     11
## 654  2020-06-02               South East     13
## 655  2020-06-03               South East     17
## 656  2020-06-04               South East     11
## 657  2020-06-05               South East     11
## 658  2020-06-06               South East     10
## 659  2020-06-07               South East     11
## 660  2020-06-08               South East      7
## 661  2020-06-09               South East     10
## 662  2020-06-10               South East     10
## 663  2020-06-11               South East      5
## 664  2020-06-12               South East      5
## 665  2020-06-13               South East      4
## 666  2020-06-14               South East      6
## 667  2020-06-15               South East      7
## 668  2020-06-16               South East     10
## 669  2020-06-17               South East      8
## 670  2020-06-18               South East      4
## 671  2020-06-19               South East      4
## 672  2020-06-20               South East      0
## 673  2020-03-01               South West      0
## 674  2020-03-02               South West      0
## 675  2020-03-03               South West      0
## 676  2020-03-04               South West      0
## 677  2020-03-05               South West      0
## 678  2020-03-06               South West      0
## 679  2020-03-07               South West      0
## 680  2020-03-08               South West      0
## 681  2020-03-09               South West      0
## 682  2020-03-10               South West      0
## 683  2020-03-11               South West      1
## 684  2020-03-12               South West      0
## 685  2020-03-13               South West      0
## 686  2020-03-14               South West      1
## 687  2020-03-15               South West      0
## 688  2020-03-16               South West      0
## 689  2020-03-17               South West      2
## 690  2020-03-18               South West      2
## 691  2020-03-19               South West      4
## 692  2020-03-20               South West      3
## 693  2020-03-21               South West      6
## 694  2020-03-22               South West      7
## 695  2020-03-23               South West      8
## 696  2020-03-24               South West      7
## 697  2020-03-25               South West      9
## 698  2020-03-26               South West     11
## 699  2020-03-27               South West     13
## 700  2020-03-28               South West     21
## 701  2020-03-29               South West     18
## 702  2020-03-30               South West     23
## 703  2020-03-31               South West     23
## 704  2020-04-01               South West     22
## 705  2020-04-02               South West     23
## 706  2020-04-03               South West     30
## 707  2020-04-04               South West     42
## 708  2020-04-05               South West     32
## 709  2020-04-06               South West     34
## 710  2020-04-07               South West     39
## 711  2020-04-08               South West     47
## 712  2020-04-09               South West     24
## 713  2020-04-10               South West     46
## 714  2020-04-11               South West     43
## 715  2020-04-12               South West     23
## 716  2020-04-13               South West     27
## 717  2020-04-14               South West     24
## 718  2020-04-15               South West     32
## 719  2020-04-16               South West     29
## 720  2020-04-17               South West     33
## 721  2020-04-18               South West     25
## 722  2020-04-19               South West     31
## 723  2020-04-20               South West     26
## 724  2020-04-21               South West     26
## 725  2020-04-22               South West     23
## 726  2020-04-23               South West     17
## 727  2020-04-24               South West     19
## 728  2020-04-25               South West     15
## 729  2020-04-26               South West     27
## 730  2020-04-27               South West     13
## 731  2020-04-28               South West     17
## 732  2020-04-29               South West     15
## 733  2020-04-30               South West     26
## 734  2020-05-01               South West      6
## 735  2020-05-02               South West      7
## 736  2020-05-03               South West     10
## 737  2020-05-04               South West     17
## 738  2020-05-05               South West     14
## 739  2020-05-06               South West     19
## 740  2020-05-07               South West     16
## 741  2020-05-08               South West      6
## 742  2020-05-09               South West     11
## 743  2020-05-10               South West      5
## 744  2020-05-11               South West      8
## 745  2020-05-12               South West      7
## 746  2020-05-13               South West      7
## 747  2020-05-14               South West      6
## 748  2020-05-15               South West      4
## 749  2020-05-16               South West      4
## 750  2020-05-17               South West      6
## 751  2020-05-18               South West      4
## 752  2020-05-19               South West      6
## 753  2020-05-20               South West      1
## 754  2020-05-21               South West      9
## 755  2020-05-22               South West      6
## 756  2020-05-23               South West      6
## 757  2020-05-24               South West      3
## 758  2020-05-25               South West      8
## 759  2020-05-26               South West     11
## 760  2020-05-27               South West      5
## 761  2020-05-28               South West     10
## 762  2020-05-29               South West      7
## 763  2020-05-30               South West      3
## 764  2020-05-31               South West      2
## 765  2020-06-01               South West      7
## 766  2020-06-02               South West      2
## 767  2020-06-03               South West      5
## 768  2020-06-04               South West      2
## 769  2020-06-05               South West      2
## 770  2020-06-06               South West      1
## 771  2020-06-07               South West      3
## 772  2020-06-08               South West      3
## 773  2020-06-09               South West      0
## 774  2020-06-10               South West      0
## 775  2020-06-11               South West      2
## 776  2020-06-12               South West      2
## 777  2020-06-13               South West      2
## 778  2020-06-14               South West      0
## 779  2020-06-15               South West      1
## 780  2020-06-16               South West      1
## 781  2020-06-17               South West      0
## 782  2020-06-18               South West      0
## 783  2020-06-19               South West      0
## 784  2020-06-20               South West      1

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-21"

The completion date of the NHS Pathways data is Sunday 21 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -9.6508  -2.6590  -0.3036   3.1029   5.1790  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.926e+00  5.292e-02   93.09   <2e-16 ***
## note_lag    1.181e-05  5.318e-07   22.20   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 11.55623)
## 
##     Null deviance: 6084.69  on 50  degrees of freedom
## Residual deviance:  583.33  on 49  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  137.816088    1.000012
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 124.094583 152.703757
## note_lag      1.000011   1.000013

Rsq(lag_mod)
## [1] 0.9041319

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1467.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.13             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.4.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.28       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.8   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.5.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.15         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.6.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.3    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0